Thiago Alcantara has moved to Anfield from Bayern Munich on a deal that cost almost £30m, and he is set to be joined by Wolves midfielder Diogo Jota who could cost in the region of £45m.
Reports on the continent have claimed that their business won’t stop there, with their eyes on a loan.
Spanish outlet Sport have reported that Liverpool want to bring in out of favour Barcelona winger Dembele on a season-long loan deal to offer support to Sadio Mane, Mohamed Salah and Roberto Firmino.
They add that Klopp is a fan of the 23-year-old former Borussia Dortmund forward, who cost the Catalan giants an initial fee of around £100m back in August of 2017.
Dembele has recovered from injury ahead of the new La Liga season, but it remains to be seen whether Ronald Koeman has any plans for the France international.
The report also says that despite the loan interest, Barcelona are unlikely to consider any offer unless it is a permanent deal.
Klopp told the BBC in relation to his potential spending last week: "Clubs are in different situations and we are living in uncertainty in the world.
"For some clubs it seems to be less important how uncertain the future is because they are owned by countries, owned by oligarchs, and that is the truth.
"We are a different kind of club. We reached the Champions League final two years ago, won it the following year and won the Premier League by being the club we are."
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And said after the confirmation of Thiago: "It's pretty simple, he is - and nobody would see it in a different way - an absolutely exceptional player.
"It's difficult, and we said that last year like we said it this year, to improve a team like us at the moment in a normal way.
"Again, it is nothing with other teams, but if you take £300 or £400 million, then we can find some players [to improve], but even then it is not easy.
"In this specific case, he is a [Liverpool] player because he brings in a different dimension in our game, that is true.”